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| /** | |
| * <b>Fixed Point Combinator is:</b> | |
| * Y = λf.(λx.f (x x)) (λx.f (x x)) | |
| * | |
| * <b>Proof of correctness:</b> | |
| * Y g = (λf . (λx . f (x x)) (λx . f (x x))) g (by definition of Y) | |
| * = (λx . g (x x)) (λx . g (x x)) (β-reduction of λf: applied main function to g) | |
| * = (λy . g (y y)) (λx . g (x x)) (α-conversion: renamed bound variable) | |
| * = g ((λx . g (x x)) (λx . g (x x))) (β-reduction of λy: applied left function to right function) | |
| * = g (Y g) (by second equality) [1] |